Multivariate Padé-approximants

AbstractFor an operator F: Rn → R, analytic in the origin, the notion of (abstract multivariate Padé-approximant (APA) is introduced, by making use of abstract polynomials. The classical Padé-approximant (n = 1) is a special case of the multivariate theory and many interesting properties of classical Padé-approximants remain valid such as covariance properties and the block-structure [Annie A. M. Cuyt, J. Oper. Theory6 (2) (1981), 207–209] of the Padé-table. Also a projection-property for multivariate Padé-approximants is proved